• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.7-16
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• 2014

Erlang-truncated exponential distribution is widely used in the field of queuing system and stochastic processes. This family of distribution include exponential distribution. In this paper we establish some exact expression and recurrence relations satisfied by the quotient moments and conditional quotient moments of the upper record values from the Erlang-truncated exponential distribution. Further a characterization of this distribution based on recurrence relations of quotient moments of record values is presented.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.347-361
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• 2014

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distribution includes exponential distribution, Pareto or Lomax distribution. In this paper, we established exact expressions and recurrence relations satised by the quotient moments of generalized order statistics for a generalized Pareto distribution. Further the results for quotient moments of order statistics and records are deduced from the relations obtained and a theorem for characterizing this distribution is presented.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.327-336
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• 2013

Generalized Pareto distributions play an important role in re-liability, extreme value theory, and other branches of applied probability and statistics. This family of distribution includes exponential distribution, Pareto distribution, and Power distribution. In this paper we establish some recurrences relations satisfied by the quotient moments of the upper record values from the generalized Pareto distribution. Further a char-acterization of this distribution based on recurrence relations of quotient moments of record values is presented.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.299-311
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• 1999

In this paper the single and product moments of order statistics of the doubly truncated Rayleigh distribution are studied. Some recurrence relations of order statistics are derived. Using order statistics, also characterization of the Rayleigh distribution are derived.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.441-451
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• 2013

In this paper, we derive recurrence relations for moments of lower generalized order statistics within a class of doubly truncated distributions. Inverse Weibull, exponentiated Weibull, power function, exponentiated Pareto, exponentiated gamma, generalized exponential, exponentiated log-logistic, generalized inverse Weibull, extended type I generalized logistic, logistic and Gumble distributions are given as illustrative examples. Further, recurrence relations for moments of order statistics and lower record values are obtained as special cases of the lower generalized order statistics, also two theorems for characterizing the general form of distribution based on single moments of lower generalized order statistics are given.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1047-1056
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• 2023

This article studies some moments characteristics of generalized order statistics for transmuted power hazard distribution. It unifies the earlier results considered by several authors. The characterization results are also outlined at the end.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.477-493
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• 2017

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random variables like order statistics and lower record values. With this definition we give simple expressions for single and product moments of dual generalized order statistics from Dagum distribution. The results for order statistics and lower records are deduced from the relations derived and some computational works are also carried out. Further, a characterizing result of this distribution on using the conditional moment of the dual generalized order statistics is discussed. These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we tabulate the means, variances, skewness and kurtosis of order statistics and record values of the Dagum distribution.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.581-588
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• 2007

We reconsider the classical orthogonal polynomials which are solutions to a second order differential equation of the form $$l_2(x)y'(x)+l_1(x)y'(x)={\lambda}_ny(x)$$. We investigate two characterization theorems of F. Marcellan et all and K.H.Kwon et al. which gave necessary and sufficient conditions on $l_1(x)\;and\;l_2(x)$ for the above differential equation to have orthogonal polynomial solutions. The purpose of this paper is to give a proof that each result in their papers respectively is equivalent.